Motorcycle won't start without jumping the solenoid

The "solenoid trick" pretty much guarantees that the solenoid is good. When you short it with the wrench you're simulating a start signal on the small terminal. When you do that the solenoid does its job, so the solenoid is probably good.

So now the question is why aren't you getting the start signal when you turn the key or hit the starter switch. Start by measuring the voltage at the terminal to see if you get anything when you ask the bike to start. Nothing at all means that you're got a problem upstream of the solenoid, perhaps a failed switch or relay (if they use one). A low voltage suggests a bad connection, could be a failing switch or relay or a poor ground. You can check for the poor ground by reading between the solenoid terminal and the battery ground post.

There is no soleniod in a motorcycle, in general. That function is done by the sprag clutch, and they rarely malfunction, and when they do it's pretty darn obvious- either the starter motor spins and nothing happens, or the motor starts and sounds like it's going to explode (and does if you run it for more than a few seconds with a seized sprag clutch).

The starter relay (which is the thing everyone is calling a solenoid) is the thing that takes the low energy signal from the button and basically connects a wrench between its posts to get the big current to flow to the starter motor. If the wrench trick works and the relay clicks when you press the button, then the relay is bad. Replace it. If the relay doesn't click, then figure out a way to tell if the relay is being energized (a voltmeter will work) and if it's getting energy, then replace it. If it's not getting energy, then the problem is further upstream in the wiring. Maybe the brake light switch.